Warm Up # 1 The perimeter of a rectangle is 32. The length is 1 more than twice the width. What are the dimensions of the rectangle? Solve the system:

Homework Check

Essential Question How can we represent the solution to a system of linear inequalities?

Graphing Linear Inequalities

We show the solution to a linear inequality with a graph. Step 1) Put the inequalities into slope-intercept form. y = mx + b slope y-intercept

Step 2) Graph the line If the inequality is < or >, make the lines dotted. If the inequality is < or >, make the lines solid.

Step 3) Shade the correct region of the graph: Above the line b) Below the line for y > or y . for y < or y ≤. **This is because more then 1 ordered pair can be a solution!

Examples: 1) y > -5x + 4

Examples: 2) x < 4 3) y ≥ -3

Systems of Inequalities

We show the solution to a system of linear inequalities with a graph!

Steps to Graphing a System of Inequalities: Put the inequalities into slope-intercept form. Decide if the lines should be dotted or solid Shade above for y > or y , shade below for y < or y ≤. Shade the overlapping section darker to show where the solutions to both inequalities lie.

Example #1: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

Graph each line, make dotted or solid and shade the correct area. Example, continued: Graph each line, make dotted or solid and shade the correct area. a: dotted shade above b: dotted shade below

#2 Graph the system of linear inequalities. x ³ –1 y > x – 2

#3 x > -2 y < 6 -2x + y > -5

#4 y ≥ -x + 4 y < 3x - 2

#5 x – y > 3 7x – y ≤ -3

#6 7x + 2y < -10 -x + 2y ≤ 11

Classwork: Solving Systems of Inequalities Worksheet Homework: Unit 7 TEST -